Dynamic Behavior of a Logistic Type Equation with Infinite Delay

A non-autonomous Logistic type equation with infinite delay is investigated.For general nonau-tonomous case,sufficient conditions which guarantee the uniform persistence and globally attractivity of thesystem are obtained;For almost periodic case,by means of a suitable Lyapunov functional,sufficient conditionsare derived for the existence and uniqueness of almost periodic solution of the system.Some new results areobtained.     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.     

捕食者一食Lotka—Volterra系统的概周期解

研究了有m个捕食者n个食饵的概周期Lotka—Volterra系统．得到了系统共存的条件．此外,还得到了系统概周期解存在唯一并且全局渐近稳定的条件．     

捕食者-食Lotka-Volterra系统的概周期解(英文)

研究了有m个捕食者n个食饵的概周期Lotka-Volterra系统.得到了系统共存的条件.此外,还得到了系统概周期解存在唯一并且全局渐近稳定的条件.     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

一类非线性微分方程的概周期解

运用Leray-Schauder不动点定理和Liapunov函数方法,研究了一类非线性微分方程的概周期解,得到了该微分方程概周期解存在的充分条件.     

具有扩散和无限时滞的Holling IV型捕食系统的概周期解

本文研究了一类具扩散和无限时滞的Holling IV型捕食系统的持续性,通过构造合适的Lyapunov函数讨论了这类系统概周期正解的存在唯一性及全局稳定性.     

具时滞扰动的高维系统概周期解的存在性、唯一性和稳定性

本文考虑了一类具时滞扰动的高维系统，利用不动点定理，建立了保证其撬周期解的存在性、唯一性和稳定性的充分性条件，推广了相关文献的主要结论．     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

一个概周期锁相环路方程的概周期解的存在唯一性和渐近稳定性

本文研究了一个概周期锁相环路方程的概周期解的存在唯一性及渐近稳定性,得到了保证系统存在唯一渐近稳定的概周期解的充分条件     

Permanence and almost periodic solution of a Lotka–Volterra model with mutual interference and time delays

In this paper, a Volterra model with mutual interference and time delays is investigated. By applying the comparison theorem of the differential equations and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Two suitable examples together with their numeric simulations are given to illustrate our results by using MatLab.     

基于比率的三种群混合扩散模型的动力学行为

讨论了一类基于比率的非自治三种群混合扩散模型,三种群间既有捕食关系又有竞争关系.我们研究了该模型的动力学行为:包括一致持久性,全局渐近稳定性,周期解,概周期解的存在唯一性.表明即使食饵种群在某些孤立的斑块中可能绝灭,也可以通过适当选取扩散率来保证系统持续生存.     

Permanence and almost periodic sequence solution for a discrete delay logistic equation with feedback control

In this paper, we consider a discrete delay logistic equation with feedback control. By applying the theory of difference inequality and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic sequence solution of the system are obtained. The result of this paper is completely new. An example is employed to illustrate our main result.     

捕食者具有阶段结构Holling II类功能性反应的捕食模型

利用重合度理论中的延拓定理讨论了捕食者具有阶段结构Holling II类功能性反应的捕食模型的正周期解的存在性,得到了保证周期解存在的充分性条件,推广了已知的相关结果. 同时通过构造Lyapunov函数得到了保证周期解稳定性的充分性条件.     

ALMOST PERIODIC SOLUTION OF A NONAUTONOMOUS MODIFIED LESLIE-GOWER PREDATOR-PREY MODEL WITH NONMONOTONIC FUNCTIONAL RESPONSE AND A PREY REFUGE

A nonautonomous modified Leslie-Gower predator-prey model with nonmonotonic functional response and a prey refuge is proposed and studied in this paper. Sufficient conditions which guarantee the permanence, extinction of the prey species and the global stability of the system are obtained, respectively. Also, by constructing a suitable Lyapunov function, some sufficient conditions are obtained for the existence of a unique globally attractive positive almost periodic solution of this model. Our results indicate that the prey refuge has positive effect on the coexistence of the species. Examples together with their numeric simulation show the feasibility of our main results.     

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.     

Permanence,extinction and periodic solution of the predator–prey system with Beddington–DeAngelis functional response and stage structure for prey

In this paper, we study the permanence, extinction and periodic solution of the periodic predator–prey system with Beddington–DeAngelis functional response and stage structure for prey. A set of sufficient and necessary conditions which guarantee the predator and prey species to be permanent are obtained. In addition, sufficient conditions are derived for the existence of positive periodic solutions to the system. Numeric simulations show the feasibility of the main results.     

具有概周期系数的三种群第Ⅱ类功能性反应的全局渐近稳定性

讨论了一类具有概周期系数的三种群第Ⅱ类功能性反应的模型，通过利用微分不等式及构造适当的李雅普诺夫函数获得了其存在全局渐近稳定性的概周期解的充分条件．     

On a theorem of Favard

We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.

     

一类具有收获率的脉冲Lotka-Volterra竞争合作系统的八个正概周期解

研究了一类具有收获率的脉冲Lotka-Volterra竞争合作系统的正概周期解.通过利用重合度理论延拓定理、概周期理论和不等式分析技巧,获得了系统至少存在8个正概周期解的充分条件,推广和改进了早期文献的相关结果.